def signcrypt(self, Reciever, params, m):
# R = g ** w mod p, w <-- Zq
w, R_value = random_pick(params.p, params.q, params.g)
# h1_R = H1(ID_R, X_R, Y_R) <-- Zq
h1_R = H1_hash(Reciever.uid, Reciever.X_u, Reciever.Y_u,
bit_length(params.q))
# T = (X_R * Y_R * (p_pub**h1_R)) ** w mod p
T_value = T_compute(Reciever.X_u, Reciever.Y_u, params.p_pub, h1_R, w,
params.p)
# C = m * T mod p
C_value = []
if bit_length(m) < bit_length(params.p):
C_value.append(t_mod(m * T_value, params.p))
else:
m_list = m2list(m, bit_length(params.p))
for x in range(len(m_list)):
C_value.append(t_mod(m_list[x] * T_value, params.p))
# h2 = H2(ID_S, T, m, C) <-- Zq
h2_value = H2_hash(self.uid, T_value, m, C_value[0],
bit_length(params.q))
# (x_S + y_S) ** -1 mod q
x_y_invert = invert(self.x_u + self.y_u, params.q)
# S = h2 * w * (x_S + y_S) ** -1 mod q
S_value = t_mod(h2_value * w * x_y_invert, params.q)
# signcryption_text = (R, C, S)
Signcryption_text = (R_value, C_value, S_value)
return Signcryption_text
class RSA:
#RSA的应用类
def keygen(self, l=2048, s=True):
while True:
p = gmpy2.mpz(Crypto.Util.number.getPrime(l))
q = gmpy2.mpz(Crypto.Util.number.getPrime(l))
n = gmpy2.mpz(p * q)
et = (p - 1) * (q - 1)
if s == True:
e = 2**16+1 # << - this is better
else:
e = 3 # << - this is bad
d = gmpy2.invert(e, et)
if d != None:
break
return (e, n), (d, n)
def encrypt(self, m, (e,n)):
#所有加密的m都是用string
m=s2i(m)
len_n = (gmpy2.bit_length(n))-1
len_m = gmpy2.bit_length(m)-1
if len_n < len_m:
pass#return [i2s(pow(s2i(m), e, n))]
else:
cs=gmpy2.powmod(m,e,n)
return cs
def unsigncrypt(self, Sender, params, Signcryption_text):
# get R, C, S
R_value = Signcryption_text[0]
C_value = Signcryption_text[1]
S_value = Signcryption_text[2]
# T' = R ** (x_R + y_R) mod p , where "un" represent the symbol '
T_value_un = powmod(R_value, t_mod(self.x_u + self.y_u, params.q),
params.p)
# T' ** -1 mod p
T_value_un_invert = invert(T_value_un, params.p)
# m' = (T' ** -1) * C mod p
m_un = t_mod(T_value_un_invert * C_value, params.p)
# h2' = H2(ID_S, T', m', C) <-- Zq
h2_value_un = H2_hash(Sender.uid, T_value_un, m_un, C_value,
bit_length(params.q))
# h1_S = H1(ID_S, X_S, Y_S) <-- Zq
h1_S = H1_hash(Sender.uid, Sender.X_u, Sender.Y_u,
bit_length(params.q))
# verify R ** h2' mod p == (X_S * Y_S * (p_pub ** h1_S)) ** S mod p
# if return true, then return m' as the plain-text
left_value = powmod(R_value, h2_value_un, params.p)
right_value = T_compute(Sender.X_u, Sender.Y_u, params.p_pub, h1_S,
S_value, params.p)
if left_value == right_value:
return m_un
def modulus (self, A):
B = np.copy(A)
p1 = B.view('uint8')
p = p1[::-1]
p = self.remove_0(p)
Pl = self.Polynomial.view('uint8')
Polynomial = Pl[::-1]
Polynomial = self.remove_0(Polynomial)
pf_bit_pos = gmpy2.bit_length(int(Polynomial[0]))
p1 = ( Polynomial >> (pf_bit_pos-1) ) & 0xff
p2 = ( Polynomial << (9 - pf_bit_pos) ) & 0xff
p1 = np.append(p1, 0)
p2 = np.append(0, p2)
pr = p1 ^ p2 & 0xff
while len(p) >= len(Polynomial):
#print p
if len(p) > len(Polynomial):
red_poly = self.Polly_table[p[0]]
for j,k in zip(red_poly, self.Polly_index):
if j != 0:
p[k] ^= j
p = p[1:]
while p[0] == 0:
if len(p) == 1:
break
p = p[1:]
else:
f_bit_pos = gmpy2.bit_length(int(p[0]))
if f_bit_pos < pf_bit_pos:
break
p1 = pr << (f_bit_pos -1) & 0xff
p2 = pr >> (9 - f_bit_pos) & 0xff
p1 = np.append(0, p1)
p2 = np.append(p2, 0)
pp = p1 ^ p2
pp = pp[1:]
if pp[-1] == 0:
pp = pp[:-1]
pp = p[:len(pp)] ^ pp
p = np.append(pp, p[len(pp):])
p = self.remove_0(p)
p = p[::-1]
q = np.append( p,np.zeros(4 - len(p)%4, dtype=np.int8))
q = np.array(q, dtype='uint8')
q = np.getbuffer(q)
q = np.frombuffer(q, dtype='uint32')
return q
def modulus (self, A):
B = np.copy(A)
p1 = B.view('uint8')
p = p1[::-1]
p = self.remove_0(p)
Pl = self.Polynomial.view('uint8')
Polynomial = Pl[::-1]
Polynomial = self.remove_0(Polynomial)
pf_bit_pos = gmpy2.bit_length(int(Polynomial[0]))
p1 = ( Polynomial >> (pf_bit_pos-1) ) & 0xff
p2 = ( Polynomial << (9 - pf_bit_pos) ) & 0xff
p1 = np.append(p1, 0)
p2 = np.append(0, p2)
pr = p1 ^ p2 & 0xff
while len(p) >= len(Polynomial):
#print p
if len(p) > len(Polynomial):
red_poly = self.Polly_table[p[0]]
for j,k in zip(red_poly, self.Polly_index):
if j != 0:
p[k] ^= j
p = p[1:]
while p[0] == 0:
if len(p) == 1:
break
p = p[1:]
else:
f_bit_pos = gmpy2.bit_length(int(p[0]))
if f_bit_pos < pf_bit_pos:
break
p1 = pr << (f_bit_pos -1) & 0xff
p2 = pr >> (9 - f_bit_pos) & 0xff
p1 = np.append(0, p1)
p2 = np.append(p2, 0)
pp = p1 ^ p2
pp = pp[1:]
if pp[-1] == 0:
pp = pp[:-1]
pp = p[:len(pp)] ^ pp
p = np.append(pp, p[len(pp):])
p = self.remove_0(p)
p = p[::-1]
q = np.append( p,np.zeros(4 - len(p)%4, dtype=np.int8))
q = np.array(q, dtype='uint8')
q = np.getbuffer(q)
q = np.frombuffer(q, dtype='uint32')
return q
def __init__(self, g, priv):
self.curve = g.curve
self.g = g
self.privkey = priv
self.pubkey = priv * g
self.Ln = bit_length(self.curve.n)
assert priv < self.curve.n - 1
def __init__(self, g, priv):
self.curve = g.curve
self.g = g
self.privkey = priv
self.pubkey = priv * g
self.Ln = bit_length(self.curve.n)
assert priv < self.curve.n - 1
def Curve_Calculation(self, Polynomial):
##### breaking of curve to give only useful information #######
Curve_Polynomial = np.array([], dtype='uint8')
Polynomial = self.str2nparray(Polynomial)
Curve_len = (len(Polynomial) - 1) * 32 + gmpy2.bit_length(
int(Polynomial[-1])) - 1
D = Polynomial.view('uint8')[::-1]
D = self.remove_0(D)
position = np.nonzero(D)
#print position
position = position[0]
secnd_chunk = 0x00
secnd_position = 0x00
frst_chunk = D[position[1]]
frst_position = (position[1] / 8) * 8 + 7 - (position[1] % 8)
if (len(position) == 3):
secnd_chunk = D[position[2]]
secnd_position = (position[2] / 8) * 8 + 7 - (position[2] % 8)
Curve_Polynomial = np.array([
Curve_len, frst_position, frst_chunk, secnd_position, secnd_chunk
],
dtype='uint8')
Curve_Polynomial = self.nparray2str2(Curve_Polynomial)
return Curve_Polynomial
def aks_test(n):
"""
Implement the AKS primality test.
"""
get_context().precision = bit_length(n)
# Check if n is a perfect power. If so, return composite.
if is_power(n):
return "composite"
# Find the smallest r such that the multiplicative order of n modulo r
# is greater than log(n, 2)^2
r = get_r(n)
# If 1 < gcd(a, n) < n for some a <= r, return composite
for a in range(1, r):
if gcd(a, n) > 1 and gcd(a, n) < n:
return "composite"
# If n <= r, return prime
if n <= r:
return "prime"
# Check if (x + a)^n mod (x^r - 1, n) != (x^n + a) mod (x^r - 1, n)
if False in ray.get([
is_congruent.remote(a, n, r)
for a in range(1, mpz(floor(sqrt(phi(r)) * log2(n))))
]):
return "composite"
return "prime"
def pollard_rho(n, process_id):
i = 1
# set the point in which rho starts
if gmpy2.bit_length(gmpy2.mpz(n)) < RHO_CONSTANT:
# small value modulo so we are better off starting with small value
if DEBUG:
print("bit size", gmpy2.bit_length(gmpy2.mpz(n)), "less than",
RHO_CONSTANT, "so non ran")
initial = process_id + 2
re_rand = False
else:
# small value modulo so we are better off starting with a random value
if DEBUG:
print("ran")
# set a flag so we can re rand rho at a latter point
re_rand = True
# process_id + 2 # this could also be random.randomint(0, n - 1)
initial = random.randint(primes[len(primes) - 1],
n // (process_id + 2))
if DEBUG:
processLock.acquire()
print("CORE", process_id, "checking rho of", initial)
processLock.release()
y = initial
k = 2
previous = initial
count = 0
while True:
i += 1
count += 1
# alt methods
# gmpy2.powmod(pow(previous, 2) - 1, 1, n) # ((pow(previous, 2)) - 1) % n #
current = (((previous**2) - 1) % n)
d = gmpy2.gcd(y - current, n)
# check to see if we've found the terminating conditions for rho and we've found a factor
if d != 1 and d != n:
return d
if i == k:
y = current
k = 2 * k
previous = current
# check to see if we are in random mode and if we need to re random
if re_rand and count > 100000: # (gmpy2.sqrt(n) // primes[len(primes)-1]):
# print("RE-RAN")
count = 0
previous = random.randint(primes[len(primes) - 1],
int(gmpy2.sqrt(n)))
def digitial_generation(self,message,Curve_Polynomial,X,Y,Order,A,d_A):
r=np.array([0x0],dtype='uint32')
m=hashlib.sha256(message).hexdigest()
Order_np = self.str2nparray(Order)
Order_int = int(Order,16)
l=(len(Order_np)-1)*32+gmpy2.bit_length(int(Order_np[-1]))
m = field.str2nparray(m)
size = l/32+1
m=self.remove_1(m)
if(l>=256):
rem=l-256
chunk_added=(rem/32)+1
m=np.append(np.zeros(chunk_added,dtype='uint32'),m)
part=32-(l+chunk_added)%32
else:
m = m[len(m)-size:]
part = 32-l%32
X1=m>>part
Y1=m<<(32-part)
Z=np.bitwise_xor(Y1[1:],X1[:-1])
Z=np.append(Z,X1[-1])
Z = self.nparray2str(Z)
Z = int(Z,16)
Z = gmpy2.f_mod(Z,Order_int)
S=0
while(S==0):
while(np.all(r[0]==0)):
k=random.randint(1,Order_int-1)
r=self.bin_public_key_gen(X,Y,A,k)
k_inv=gmpy2.invert(k,Order_int)
r = self.nparray2str(r[0])
r = int(r,16)
r=gmpy2.f_mod(r,Order_int)
rd_A = gmpy2.mul(r,d_A)
rd_A = gmpy2.f_mod(rd_A,Order_int)
Zrd_A = rd_A + Z
Zrd_A = int(Zrd_A)
k_inv = int(k_inv)
S = gmpy2.mul(Zrd_A,k_inv)
S = gmpy2.f_mod(S,Order_int)
return r,S
def digitial_generation(self,message,Curve_Polynomial,X,Y,Order,A,d_A):
r=np.array([0x0],dtype='uint32')
m=hashlib.sha256(message).hexdigest()
Order_np = self.str2nparray(Order)
Order_int = int(Order,16)
l=(len(Order_np)-1)*32+gmpy2.bit_length(int(Order_np[-1]))
m = field.str2nparray(m)
size = l/32+1
m=self.remove_1(m)
if(l>=256):
rem=l-256
chunk_added=(rem/32)+1
m=np.append(np.zeros(chunk_added,dtype='uint32'),m)
part=32-(l+chunk_added)%32
else:
m = m[len(m)-size:]
part = 32-l%32
X1=m>>part
Y1=m<<(32-part)
Z=np.bitwise_xor(Y1[1:],X1[:-1])
Z=np.append(Z,X1[-1])
Z = self.nparray2str(Z)
Z = int(Z,16)
Z = gmpy2.f_mod(Z,Order_int)
S=0
while(S==0):
while(np.all(r[0]==0)):
k=random.randint(1,Order_int-1)
r=self.bin_public_key_gen(X,Y,A,k)
k_inv=gmpy2.invert(k,Order_int)
r = self.nparray2str(r[0])
r = int(r,16)
r=gmpy2.f_mod(r,Order_int)
rd_A = gmpy2.mul(r,d_A)
rd_A = gmpy2.f_mod(rd_A,Order_int)
Zrd_A = rd_A + Z
Zrd_A = int(Zrd_A)
k_inv = int(k_inv)
S = gmpy2.mul(Zrd_A,k_inv)
S = gmpy2.f_mod(S,Order_int)
return r,S
def digitial_Verification(self,message,Order,X,Y,A,d_A,r,S):
X=self.str2nparray(X)
Y=self.str2nparray(Y)
A=self.str2nparray(A)
m=hashlib.sha256(message).hexdigest()
Order_np = self.str2nparray(Order)
Order_int = int(Order,16)
l=(len(Order_np)-1)*32+gmpy2.bit_length(int(Order_np[-1]))
m = field.str2nparray(m)
size = l/32+1
m=self.remove_1(m)
if(l>=256):
rem=l-256
chunk_added=(rem/32)+1
m=np.append(np.zeros(chunk_added,dtype='uint32'),m)
part=32-(l+chunk_added)%32
else:
m = m[len(m)-size:]
part = 32-l%32
X1=m>>part
Y1=m<<(32-part)
Z=np.bitwise_xor(Y1[1:],X1[:-1])
Z=np.append(Z,X1[-1])
Z = self.nparray2str(Z)
Z = int(Z,16)
Z = gmpy2.f_mod(Z,Order_int) #####Truncated Message
w=gmpy2.invert(S,Order_int)
u1 = gmpy2.mul(Z,w)
u1 = gmpy2.f_mod(u1,Order_int)
u2 = gmpy2.mul(r,w)
u2 = gmpy2.f_mod(u2,Order_int)
Q_A=self.public_key_gen(X,Y,A,d_A) #Q_A = d_A * G
X1=self.public_key_gen(X,Y,A,int(u1))
X2=self.public_key_gen(Q_A[0],Q_A[1],A,int(u2)) #u2*Q_A
X3=self.point_add(X1[0],X1[1],X2[0],X2[1],A)
X3=self.nparray2str(X3[0])
X3 = gmpy2.f_mod(int(X3,16),Order_int)
#print X3[0]
return X3
def data_format_bind(x, y, bits): len_y = bit_length(y) x_bin = bin(x << (bits - len_y)) x_bin_str = str(x_bin) y_bin = bin(y) y_bin_str = str(y_bin) x_y_bind_str = x_bin_str[2:] + y_bin_str[2 :] x_y_bind = mpz(x_y_bind_str, 2) return x_y_bind
def digitial_Verification(self,message,Order,X,Y,A,d_A,r,S):
X=self.str2nparray(X)
Y=self.str2nparray(Y)
A=self.str2nparray(A)
m=hashlib.sha256(message).hexdigest()
Order_np = self.str2nparray(Order)
Order_int = int(Order,16)
l=(len(Order_np)-1)*32+gmpy2.bit_length(int(Order_np[-1]))
m = field.str2nparray(m)
size = l/32+1
m=self.remove_1(m)
if(l>=256):
rem=l-256
chunk_added=(rem/32)+1
m=np.append(np.zeros(chunk_added,dtype='uint32'),m)
part=32-(l+chunk_added)%32
else:
m = m[len(m)-size:]
part = 32-l%32
X1=m>>part
Y1=m<<(32-part)
Z=np.bitwise_xor(Y1[1:],X1[:-1])
Z=np.append(Z,X1[-1])
Z = self.nparray2str(Z)
Z = int(Z,16)
Z = gmpy2.f_mod(Z,Order_int) #####Truncated Message
w=gmpy2.invert(S,Order_int)
u1 = gmpy2.mul(Z,w)
u1 = gmpy2.f_mod(u1,Order_int)
u2 = gmpy2.mul(r,w)
u2 = gmpy2.f_mod(u2,Order_int)
Q_A=self.public_key_gen(X,Y,A,d_A) #Q_A = d_A * G
X1=self.public_key_gen(X,Y,A,int(u1))
X2=self.public_key_gen(Q_A[0],Q_A[1],A,int(u2)) #u2*Q_A
X3=self.point_add(X1[0],X1[1],X2[0],X2[1],A)
X3=self.nparray2str(X3[0])
X3 = gmpy2.f_mod(int(X3,16),Order_int)
#print X3[0]
return X3
def signcrypt( self, Reciever, params, m): # R = g ** w mod p, w <-- Zq w, R_value = random_pick(params.p, params.q, params.g) # h1_R = H1(ID_R, X_R, Y_R) <-- Zq h1_R = H1_hash(Reciever.uid, Reciever.X_u, Reciever.Y_u, bit_length(params.q)) # V = (X_R * Y_R * (p_pub**h1_R)) ** w mod p V_value = V_compute(Reciever.X_u, Reciever.Y_u, params.p_pub, h1_R, w, params.p) # h3 = H3(V) <-- Zq h3_value = H3_hash( V_value, bit_length( params.p )) # d = H4(ID_S, m, X_S, R) <-- Zq d_value = H4_hash(self.uid, m, self.X_u, R_value, bit_length(params.q)) # f = H4(ID_S, m, Y_S, R) <-- Zq f_value = H4_hash(self.uid, m, self.Y_u, R_value, bit_length(params.q)) # U = d * (x_a + y_a) + w * f mod q U_value = t_mod((d_value * (self.x_u + self.y_u) + w * f_value), params.q) # m || U m_u_value = data_format_bind(m, U_value, bit_length(params.q)) # C = H3(V) (+) m || U C_value = h3_value ^ m_u_value # h2 = H2(ID_a, R, C) <-- Zq h2_value = H2_hash(self.uid, R_value, C_value, bit_length(params.q)) # S = w * ((x_a + y_a +h2) ** -1) mod q x_y_h_invert = invert(self.x_u + self.y_u + h2_value, params.q) S_value = t_mod(w * x_y_h_invert, params.q) # signcryption_text = (h2, S, C) Signcryption_text = (h2_value, S_value, C_value) return Signcryption_text
def unsigncrypt( self, Sender, params, Signcryption_text): # get h2, S, C h2_value = Signcryption_text[0] S_value = Signcryption_text[1] C_value = Signcryption_text[2] # h1_S = H1(ID_S, X_S, Y_S) <-- Zq h1_S = H1_hash(Sender.uid, Sender.X_u, Sender.Y_u, bit_length(params.q)) # R' = (X_S * Y_S * (p_pub**h1_S) * (g ** h2)) ** w mod p, un represent ' temp = powmod(params.g, h2_value, params.p) temp = t_mod(temp * Sender.Y_u, params.p) R_value_un = V_compute(Sender.X_u, temp, params.p_pub, h1_S, S_value, params.p) # V' = R' ** (x_b + y_b) mod q V_value_un = powmod(R_value_un, t_mod(self.x_u + self.y_u, params.q), params.p) # h3 = H3(V') <-- Zp h3_value = H3_hash(V_value_un, bit_length(params.p)) # m || U = C (+) h3 m_u_value_un = C_value ^ h3_value # get m' m_un = m_u_value_un >> bit_length(params.q) # get U' U_value_un = (m_un << bit_length(params.q)) ^ m_u_value_un # d' = H4(ID_a, m', X_a, R) <-- Zq d_value_un = H4_hash(Sender.uid, m_un, Sender.X_u, R_value_un, bit_length(params.q)) # f' = H4(ID_a, m', Y_a, R) <-- Zq f_value_un = H4_hash(Sender.uid, m_un, Sender.Y_u, R_value_un, bit_length(params.q)) # verify g ** U' == ((X_a * Y_a * (p_pub ** h1_a)) ** d') * (R' ** f') mod p # if return true, then return m'; else return None left_value = powmod(params.g, U_value_un, params.p) temp1 = V_compute(Sender.X_u, Sender.Y_u, params.p_pub, h1_S, d_value_un, params.p) temp2 = powmod(R_value_un, f_value_un, params.p) right_value = t_mod(temp1 * temp2, params.p) if left_value == right_value : return m_un
def m2list(m, bits):
m_len = bit_length(m)
m_number = m_len // (bits - 2) + 1
m_bin_str = bin(m)
m_list = []
for x in range(m_number):
if x != m_number - 1:
temp_str = '1' + m_bin_str[(2 + x * (bits - 2)):(2 + (x + 1) *
(bits - 2))]
m_list.append(mpz(temp_str, 2))
else:
temp_str = '1' + m_bin_str[(2 + x * (bits - 2)):]
m_list.append(mpz(temp_str, 2))
return m_list
def bin_inverse(self,A):
p=self.Polynomial.tolist()
while p[-1] == 0:
if len(p) == 1:
break
p = p[:-1]
length=len(p)*32-32+gmpy2.bit_length(p[-1])-1
A=self.str2nparray(A)
array=self.baumer_chain(length)
C=self.inverse1(A)
return C
def bin_inverse(self,A):
p=self.Polynomial.tolist()
while p[-1] == 0:
if len(p) == 1:
break
p = p[:-1]
length=len(p)*32-32+gmpy2.bit_length(p[-1])-1
A=self.str2nparray(A)
array=self.baumer_chain(length)
C=self.inverse1(A)
return C
def public_key_gen(self,x,y,a,n):
sq=[]
sq_x=[]
public_key=[]
bit_len = gmpy2.bit_length(n)
####public key generation #########3
if(n&0x1):
sq_x.append(x)
sq_x.append(y)
for i in range(1,bit_len):
if((n>>i)&0x01):
sq=self.point_doubl(x,y,a)
sq_x.append(sq[0])
sq_x.append(sq[1])
x=sq[0]
y=sq[1]
else:
sq=self.point_doubl(x,y,a)
x=sq[0]
y=sq[1]
j=0
sq=[]
if(len(sq_x)==2):
return sq_x[-2:]
x2=sq_x[2]
y2=sq_x[3]
for i in range(len(sq_x)/2-1):
sq = self.point_add(sq_x[j],sq_x[j+1],x2,y2,a)
public_key.append(sq[0])
public_key.append(sq[1])
if(i==0):
j=j+4
else:
j=j+2
x2=(sq[0])
y2=(sq[1])
return public_key[-2:]
def public_key_gen(self,x,y,a,n):
sq=[]
sq_x=[]
public_key=[]
bit_len = gmpy2.bit_length(n)
####public key generation #########3
if(n&0x1):
sq_x.append(x)
sq_x.append(y)
for i in range(1,bit_len):
if((n>>i)&0x01):
sq=self.point_doubl(x,y,a)
sq_x.append(sq[0])
sq_x.append(sq[1])
x=sq[0]
y=sq[1]
else:
sq=self.point_doubl(x,y,a)
x=sq[0]
y=sq[1]
j=0
sq=[]
if(len(sq_x)==2):
return sq_x[-2:]
x2=sq_x[2]
y2=sq_x[3]
for i in range(len(sq_x)/2-1):
sq = self.point_add(sq_x[j],sq_x[j+1],x2,y2,a)
public_key.append(sq[0])
public_key.append(sq[1])
if(i==0):
j=j+4
else:
j=j+2
x2=(sq[0])
y2=(sq[1])
return public_key[-2:]
def inverse1(self,A):
P=self.remove_1(self.Polynomial)
l=((len(P)-1)*32)+gmpy2.bit_length(int(P[-1]))-1
array = self.baumer_chain(l)
count=0
inv_array=np.array([A],dtype='uint32')
prev=np.copy(A)
#print array
for i in range(0,len(array)-1,2):
#print i
x=array[i]
y=array[i+1]
var=y #how many time squaring
#print var,x,y
n=prev
while(var!=0):
var=var-1
sqr=self.modulus(self.square(n))
n=sqr
#break
if(y==1):
f=A
else:
f=prev
#print f,d
mul=self.modulus(self.multiplication(f,sqr))
count+=1
prev=mul
final=self.modulus(self.square(prev))
#print "number of multiplication",count
#print prev
#print x,y
return final
def inverse1(self,A):
P=self.remove_1(self.Polynomial)
l=((len(P)-1)*32)+gmpy2.bit_length(int(P[-1]))-1
array = self.baumer_chain(l)
count=0
inv_array=np.array([A],dtype='uint32')
prev=np.copy(A)
#print array
for i in range(0,len(array)-1,2):
#print i
x=array[i]
y=array[i+1]
var=y #how many time squaring
#print var,x,y
n=prev
while(var!=0):
var=var-1
sqr=self.modulus(self.square(n))
n=sqr
#break
if(y==1):
f=A
else:
f=prev
#print f,d
mul=self.modulus(self.multiplication(f,sqr))
count+=1
prev=mul
final=self.modulus(self.square(prev))
#print "number of multiplication",count
#print prev
#print x,y
return final
def generate_strong_strong_prime(seed, min_bitsize, strong_strong_integers,
number_of_strong_strong_integers, gamma, PI):
"""Return a strong strong prime deterministically determined from the input parameters, and what remains of the seed.
Depending on the target prime size "min_bitsize", we need to find the appropriate table of first primes
[p_0,...,p_{f-2},p_{f-1}] such that PI = p_0 * ... * p_{f-1} is larger than 2**(min_bitsize-2), but such that p_0 *
... * p_{f-2} is not. We'll store the primes in a table called "first_primes", such that first_primes[i] = p_i. The
variable "strong_strong_integers" will be a list of lists, such that strong_strong_integers[i] is the list of
integers r such that r, 2r+1 and 2(2r+1)+1 are invertible modulo first_primes[i]. Taking the inverse CRT on any
[c_0,c_1,...,c_{f-1}] = [strong_strong_integers[0][i],strong_strong_integers[1][j],...,strong_strong_integers[f-1][k]]
gives an integer c such that c, 2c+1, and 4c+3 are invertible modulo PI, which makes c a good candidate for being
a strong strong prime generator (i.e., 4c+3 a good candidate for being a strong strong prime). The seed allows to
determine in initial array [c_0,c_1,...,c_{f-1}] and thus an initial candidate c. Going from one such array to the
other is done deterministically.
"""
# Consume the seed and update it
(indexes,
seed) = list_of_indexes_from_seed(seed, number_of_strong_strong_integers)
candidate_nbr = 0
while True:
alpha = [x[i] for x, i in zip(strong_strong_integers, indexes)
] # alpha is in Z2* x Z3* x Z5* x ..... Apply the inverse CRT
c = sum([x * y for x, y in zip(alpha, gamma)]) % PI
candidate_nbr += 1
if gmpy2.bit_length(
c
) >= min_bitsize - 2 and subroutines.is_strong_strong_prime_generator(
c):
break
indexes = next_indexes(indexes, number_of_strong_strong_integers)
print("\tThe successful candidate is the number %d" % (candidate_nbr))
return (4 * c + 3, seed)
def Curve_Calculation(self,Polynomial):
##### breaking of curve to give only useful information #######
Curve_Polynomial=np.array([],dtype='uint8')
Polynomial=self.str2nparray(Polynomial)
Curve_len=(len(Polynomial)-1)*32+gmpy2.bit_length(int(Polynomial[-1]))-1
D=Polynomial.view('uint8')[::-1]
D=self.remove_0(D)
position=np.nonzero(D)
#print position
position=position[0]
secnd_chunk=0x00
secnd_position=0x00
frst_chunk=D[position[1]]
frst_position=(position[1]/8)*8+7-(position[1]%8)
if(len(position)==3):
secnd_chunk=D[position[2]]
secnd_position=(position[2]/8)*8+7-(position[2]%8)
Curve_Polynomial=np.array([Curve_len,frst_position,frst_chunk,secnd_position,secnd_chunk],dtype='uint8')
Curve_Polynomial=self.nparray2str2(Curve_Polynomial)
return Curve_Polynomial
def william_p1(n, process_id):
# this algorithm technically works but literally none of the modulos were p+1 so idk
# choose a B (work limit) to start with
if gmpy2.bit_length(gmpy2.mpz(n)) <= 2044:
work_limit = pow(n, (1 / 6))
else:
work_limit = gmpy2.div(n, 27)
threshold = 3
previous_sub2 = 2
# A needs to be greater than 2 to start with so we therefore start with 3
A = process_id + 3
previous = A
counter = 0
# if the counter ever reaches m, terminate
while counter != threshold:
counter += 1
# current = (a^(current-1) - current-2) % n)
current = (((A**previous) - previous_sub2) % n)
# move the previous variables forward
previous_sub2 = previous
previous = current
d = gmpy2.gcd(current - 2, n)
if d != 1 and d != n:
# calculate the factorial of m
mult = gmpy2.fac(threshold)
if DEBUG:
print(d, mult)
# check to see if we've found the terminating conditions for p + 1
if gmpy2.f_mod(mult, d):
return d
else:
# increment threshold by 1 if we haven't found anything
threshold += 1
if threshold > work_limit:
return 1
return 1
def pollard_p1(n, process_id):
# choose a B (work limit) to start with
if gmpy2.bit_length(gmpy2.mpz(n)) <= 2044:
work_limit = pow(n, (1 / 6))
else:
work_limit = gmpy2.div(n, 27)
a = 2
# break up how many things we have to check so we can split over cores
process_range = (math.floor(work_limit) // PROCESS_COUNT)
start = process_range * process_id
end = process_range * (process_id + 1) - 1
# assign default values here so we are an excellent, coding standard following coder
q1, q2, q3 = 0, 0, 0
if DEBUG:
# lock processes so we can print cleanly (thanks 421)
processLock.acquire()
print("CORE", process_id, "checking p1 from", start, "to", end)
processLock.release()
# calculate the quarter ranges
q1 = ((process_range // 4) * 1) + start
q2 = ((process_range // 4) * 2) + start
q3 = ((process_range // 4) * 3) + start
for i in range(start, end):
# print informative debug statements
if DEBUG:
if i == q1:
print("CORE", process_id, "p1 25%")
elif i == q2:
print("CORE", process_id, "p1 50%")
elif i == q3:
print("CORE", process_id, "p1 75%")
# check to see if we've found the terminating conditions for p - 1
a = gmpy2.powmod(a, i, n)
d = gmpy2.gcd(a - 1, n)
if d != 1 and d != n:
return d
return 1
def generate_strong_strong_prime(seed, min_bitsize,strong_strong_integers,number_of_strong_strong_integers,gamma,PI):
"""Return a strong strong prime deterministically determined from the input parameters, and what remains of the seed.
Depending on the target prime size "min_bitsize", we need to find the appropriate table of first primes
[p_0,...,p_{f-2},p_{f-1}] such that PI = p_0 * ... * p_{f-1} is larger than 2**(min_bitsize-2), but such that p_0 *
... * p_{f-2} is not. We'll store the primes in a table called "first_primes", such that first_primes[i] = p_i. The
variable "strong_strong_integers" will be a list of lists, such that strong_strong_integers[i] is the list of
integers r such that r, 2r+1 and 2(2r+1)+1 are invertible modulo first_primes[i]. Taking the inverse CRT on any
[c_0,c_1,...,c_{f-1}] = [strong_strong_integers[0][i],strong_strong_integers[1][j],...,strong_strong_integers[f-1][k]]
gives an integer c such that c, 2c+1, and 4c+3 are invertible modulo PI, which makes c a good candidate for being
a strong strong prime generator (i.e., 4c+3 a good candidate for being a strong strong prime). The seed allows to
determine in initial array [c_0,c_1,...,c_{f-1}] and thus an initial candidate c. Going from one such array to the
other is done deterministically.
"""
# Consume the seed and update it
(indexes, seed) = list_of_indexes_from_seed(seed, number_of_strong_strong_integers)
candidate_nbr = 0
while True:
alpha = [x[i] for x, i in zip(strong_strong_integers, indexes)] # alpha is in Z2* x Z3* x Z5* x ..... Apply the inverse CRT
c = sum([x*y for x, y in zip(alpha, gamma)]) % PI
candidate_nbr += 1
if gmpy2.bit_length(c) >= min_bitsize-2 and subroutines.is_strong_strong_prime_generator(c):
break
indexes = next_indexes(indexes, number_of_strong_strong_integers)
print("\tThe successful candidate is the number %d"%(candidate_nbr))
return (4*c + 3,seed)
alice_public_exponent, alice_modulus))
log.info("Bob public key has public exponent {} and modulus {}".format(
bob_public_exponent, bob_modulus))
# Get K1 and K2 in multi-precision form
res_k1 = iroot(mpz(Converter.bytes_to_int(c1)), alice_public_exponent)
res_k2 = iroot(mpz(Converter.bytes_to_int(c2)), bob_public_exponent)
if (res_k1[1] and res_k2[1]):
# Convert results to bytes
k1 = Converter.swap_endianness(to_binary(res_k1[0]))[:-2]
k2 = Converter.swap_endianness(to_binary(res_k2[0]))[:-2]
# Log
log.success("Finded K1, with effective length of {} bits, is {}".format(
bit_length(res_k1[0]), Converter.bytes_to_hex(k1)))
log.success("Finded k2, with effective length of {} bits, is: {}".format(
bit_length(res_k2[0]), Converter.bytes_to_hex(k2)))
else:
# Force exitW
log.failure("Failed to obtain K1 and K2")
exit(0)
# Compute key used in AES
xor = bytes([_k1_char ^ _k2_char for _k1_char, _k2_char in zip(k1, k2)])
log.info("XOR between K1 and K2 is: {}".format(Converter.bytes_to_hex(xor)))
k = SHA256.new(xor).digest()
log.info("Key used for AES encryption is: {}".format(
Converter.bytes_to_hex(k)))
def gen_mod_table(self):
index = 0
p = self.Polynomial.view('uint8')
p = p[::-1]
while (p[0] == 0):
if (len(p) == 1):
break
p = p[1:]
f_bit_pos = gmpy2.bit_length(int(p[0]))
self.Polly_byte_len = len(p)
self.Polly_bit_len = f_bit_pos
p = np.array(p)
p1 = p >> (f_bit_pos-1)
p2 = p << (9 - f_bit_pos)
p1 = np.append(p1, 0)
p2 = np.append(0, p2)
pr = p1 ^ p2 & 0xff
p1 = pr >> 1
p2 = pr << 7
p1 = np.append(p1, 0)
p2 = np.append(0, p2)
pl = (p1 ^ p2) & 0xff
pl = pl[1:]
pl[0] = pl[0] & 0x7F
self.pr = pr
poly_7 = []
p3 = np.append(0, pr[1:])
poly_7.append(p3)
for i in range(7):
p1 = p3 << (1)
p2 = p3 >> (7)
p2 = np.append(p2[1:], 0)
p3 = (p1 ^ p2) & 0xff
if not p3[0] == 0:
p3 = p3 ^ pr
poly_7.append(p3)
index = []
for i in range(len(poly_7[0])):
for j in poly_7:
if j[i] != 0:
index.append(i)
break
Polly_table = []
for i in range(256):
val = np.zeros(len(poly_7[0]), dtype='uint8')
for j in range(8):
if ((i >> j) & 0x1):
val = val ^ poly_7[j]
indexed_val = []
for k in index:
indexed_val.append(val[k])
Polly_table.append(np.array(indexed_val))
self.Polly_table = Polly_table
self.Polly_index = index
return 0
bits = 512 # 1024/2
e = 0x3
while True:
p,q = gmpy2.mpz(getPrime(bits)), gmpy2.mpz(getPrime(bits))
N = gmpy2.mpz(p * q)
phi = (p - 1) * (q - 1)
if gcd(e, phi) == 1:
break
#print e, phi
d = gmpy2.invert(e, phi)
return (e, N), (d, N)
def rsa_enc(m, (e, N)):
m = a2i(m)
len_m = gmpy2.bit_length(m) - 1
len_n = gmpy2.bit_length(N) - 1
if len_n < len_m: # if message is bigger than N
pass
else:
c = gmpy2.powmod(m, e, N)
return c
def rsa_dec(c, (d, N)):
m = gmpy2.powmod(c, d, N)
return i2a(m)
def a2i(m):
# transform ASCII to int.
return int(m.encode('hex'), 16)
def i2a(i):
def main():
# Test local versions of libraries
utils.test_python_version()
utils.test_gmpy2_version()
utils.test_pari_version()
utils.test_pari_seadata()
now = datetime.now()
# Parse command line arguments
parser = argparse.ArgumentParser(description="Generate an Edwards curve over a given prime field, suited for cryptographic purposes.")
parser.add_argument("input_file",
help="""JSON file containing the BBS parameters and the prime of the underlying field (typically, the output of
03_generate_prime_field_using_bbs.py.
""")
parser.add_argument("output_file", help="Output file where this script will write the parameter d of the curve and the current BBS parameters.")
parser.add_argument("--start",
type=int,
help="Number of the candidate to start with (default is 1).",
default=1)
parser.add_argument("--max_nbr_of_tests",
type=int,
help="Number of candidates to test before stopping the script (default is to continue until success).")
parser.add_argument("--fast",
help=""" While computing a the curve cardinality with SAE, early exit when the cardinality will obviously be divisible by
a small integer > 4. This reduces the time required to find the final curve, but the
cardinalities of previous candidates are not fully computed.
""",
default=False,
action="store_true")
args = parser.parse_args()
# Check arguments
print("Checking inputs...")
output_file = args.output_file
if os.path.exists(output_file):
utils.exit_error("The output file '%s' already exists. Exiting."%(output_file))
input_file = args.input_file
with open(input_file, "r") as f:
data = json.load(f)
# Declare a few important variables
bbs_p = int(data["bbs_p"])
bbs_q = int(data["bbs_q"])
bbs_n = bbs_p * bbs_q
bbs_s = int(data["bbs_s"]) % bbs_n
p = int(data["p"])
start = max(int(args.start),1)
max_nbr_of_tests = None
if args.max_nbr_of_tests:
max_nbr_of_tests = int(args.max_nbr_of_tests)
if not subroutines.is_strong_strong_prime(bbs_p):
utils.exit_error("bbs_p is not a strong strong prime.")
if not subroutines.is_strong_strong_prime(bbs_q):
utils.exit_error("bbs_q is not a strong strong prime.")
if not (subroutines.deterministic_is_pseudo_prime(p) and p%4 == 3):
utils.exit_error("p is not a prime congruent to 3 modulo 4.")
# Initialize BBS
print("Initializing BBS...")
bbs = bbsengine.BBS(bbs_p, bbs_q, bbs_s)
# Info about the prime field
utils.colprint("Prime of the underlying prime field:", "%d (size: %d)"%(p, gmpy2.bit_length(p)))
size = gmpy2.bit_length(p) # total number of bits queried to bbs for each test
# Skip the first "start" candidates
candidate_nbr = start-1
bbs.skipbits(size * (start-1))
# Start looking for "d"
while True:
if max_nbr_of_tests and candidate_nbr >= start + max_nbr_of_tests - 1:
print("Did not find an adequate parameter, starting at candidate %d (included), limiting to %d candidates."%(start, max_nbr_of_tests))
utils.exit_error("Last candidate checked was number %d."%(candidate_nbr))
candidate_nbr += 1
bits = bbs.genbits(size)
d = 0
for bit in bits:
d = (d << 1) | bit
print("The candidate number %d is d = %d (ellapsed time: %s)"%(candidate_nbr, d, str(datetime.now()-now)))
# Test 1
if not utils.check(d != 0 and d < p, "d != 0 and d < p", 1):
continue
# Test 2
if not utils.check(gmpy2.legendre(d, p) == -1, "d is not a square modulo p", 2):
continue
# Test 3
if args.fast:
cardinality = subroutines.sea_edwards(1, d, p, 4)
else:
cardinality = subroutines.sea_edwards(1, d, p)
assert(cardinality % 4 == 0)
q = cardinality>>2
if not utils.check(subroutines.deterministic_is_pseudo_prime(q), "The curve cardinality / 4 is prime", 3):
continue
# Test 4
trace = p+1-cardinality
cardinality_twist = p+1+trace
assert(cardinality_twist % 4 == 0)
q_twist = cardinality_twist>>2
if not utils.check(subroutines.deterministic_is_pseudo_prime(q_twist), "The twist cardinality / 4 is prime", 4):
continue
# Test 5
if not utils.check(q != p and q_twist != p, "Curve and twist are safe against additive transfer", 5):
continue
# Test 6
embedding_degree = subroutines.embedding_degree(p, q)
if not utils.check(embedding_degree > (q-1) // 100, "Curve is safe against multiplicative transfer", 6):
continue
# Test 7
embedding_degree_twist = subroutines.embedding_degree(p, q_twist)
if not utils.check(embedding_degree_twist > (q_twist-1) // 100, "Twist is safe against multiplicative transfer", 7):
continue
# Test 8
D = subroutines.cm_field_discriminant(p, trace)
if not utils.check(abs(D) >= 2**100, "Absolute value of the discriminant is larger than 2^100", 8):
continue
break
# Find a base point
while True:
bits = bbs.genbits(size)
y = 0
for bit in bits:
y = (y<<1) | bit
u = int((1 - y**2) * gmpy2.invert(1 - d*y**2, p)) % p
if gmpy2.legendre(u, p) == -1:
continue
x = gmpy2.powmod(u, (p+1) // 4, p)
(x,y) = subroutines.add_on_edwards(x, y, x, y, d, p)
(x,y) = subroutines.add_on_edwards(x, y, x, y, d, p)
if (x, y) == (0, 1):
continue
assert((x**2 + y**2) % p == (1 + d*x**2*y**2) % p)
break
# Print some informations
utils.colprint("Number of the successful candidate:", str(candidate_nbr))
utils.colprint("Edwards elliptic curve parameter d is:", str(d))
utils.colprint("Number of points:", str(cardinality))
utils.colprint("Number of points on the twist:", str(cardinality_twist))
utils.colprint("Embedding degree of the curve:", "%d"%embedding_degree)
utils.colprint("Embedding degree of the twist:", "%d"%embedding_degree_twist)
utils.colprint("Discriminant:", "%d"%D)
utils.colprint("Trace:", "%d"%trace)
utils.colprint("Base point coordinates:", "(%d, %d)"%(x, y))
# Save p, d, x, y, etc. to the output_file
print("Saving the parameters to %s"%output_file)
bbs_s = bbs.s
with open(output_file, "w") as f:
json.dump({"p": int(p),
"bbs_p": int(bbs_p),
"bbs_q": int(bbs_q),
"bbs_s": int(bbs_s),
"candidate_nbr": int(candidate_nbr),
"d": int(d),
"cardinality": cardinality,
"cardinality_twist": cardinality_twist,
"embedding_degree": embedding_degree,
"embedding_degree_twist": embedding_degree_twist,
"discriminant": D,
"trace": trace,
"base_point_x": x,
"base_point_y": y},
f,
sort_keys=True)
def partialkey_compute(self, User):
r_u, User.Y_u = random_pick(self.p, self.q, self.g)
User.y_u = t_mod((r_u + t_mod(
self.s * H1_hash(User.uid, User.X_u, User.Y_u, bit_length(self.q)),
self.q)), self.q)
def main():
# Test local versions of libraries
utils.test_python_version()
utils.test_gmpy2_version()
# Parse command line arguments
parser = argparse.ArgumentParser(description="Generate a prime field, suited for being the underlying field of a twist-secure Edwards curve.")
parser.add_argument("input_file", help="JSON file containing the BBS parameters (typically, the output of 02_generate_bbs_parameters.py).")
parser.add_argument("output_file", help="Output file where this script will write the prime of the field and the current BBS parameters.")
parser.add_argument("prime_size", type=int, help="Size of the prime (e.g. 256 bits)")
args = parser.parse_args()
# Check arguments
output_file = args.output_file
if os.path.exists(output_file):
utils.exit_error("The output file '%s' already exists. Exiting."%(output_file))
size = int(args.prime_size)
input_file = args.input_file
with open(input_file, "r") as f:
data = json.load(f)
bbs_p = int(data["bbs_p"])
bbs_q = int(data["bbs_q"])
bbs_n = bbs_p * bbs_q
bbs_s = int(data["bbs_s"]) % bbs_n
# Check inputs
print("Checking inputs...")
if not subroutines.is_strong_strong_prime(bbs_p):
utils.exit_error("bbs_p is not a strong strong prime.")
if not subroutines.is_strong_strong_prime(bbs_q):
utils.exit_error("bbs_q is not a strong strong prime.")
# Initialize BBS
bbs = bbsengine.BBS(bbs_p, bbs_q, bbs_s)
# generate a "size"-bit prime "p"
candidate_nbr = 0
print("Generating a prime field Fp (where p is congruent to 3 mod 4)...")
while True:
candidate_nbr += 1
bits = [1] + bbs.genbits(size-3) + [1,1]
assert(len(bits) == size)
p = 0
for bit in bits:
p = (p << 1) | bit
assert(p % 4 == 3)
assert(gmpy2.bit_length(p) == size)
if subroutines.deterministic_is_pseudo_prime(p):
break
utils.colprint("%d-bit prime found:"%size, str(p))
utils.colprint("The good candidate was number: ", str(candidate_nbr))
# Save p and the current bbs parameters to the output_file
print("Saving p and the BBS parameters to %s"%(output_file))
bbs_s = bbs.s
with open(output_file, "w") as f:
json.dump({"p": int(p),
"bbs_p": int(bbs_p),
"bbs_q": int(bbs_q),
"bbs_s": int(bbs_s)},
f,
sort_keys=True)
def gen_mod_table(self):
index = 0
p = self.Polynomial.view('uint8')
p = p[::-1]
while (p[0] == 0):
if (len(p) == 1):
break
p = p[1:]
f_bit_pos = gmpy2.bit_length(int(p[0]))
self.Polly_byte_len = len(p)
self.Polly_bit_len = f_bit_pos
p = np.array(p)
p1 = p >> (f_bit_pos-1)
p2 = p << (9 - f_bit_pos)
p1 = np.append(p1, 0)
p2 = np.append(0, p2)
pr = p1 ^ p2 & 0xff
p1 = pr >> 1
p2 = pr << 7
p1 = np.append(p1, 0)
p2 = np.append(0, p2)
pl = (p1 ^ p2) & 0xff
pl = pl[1:]
pl[0] = pl[0] & 0x7F
self.pr = pr
poly_7 = []
p3 = np.append(0, pr[1:])
poly_7.append(p3)
for i in range(7):
p1 = p3 << (1)
p2 = p3 >> (7)
p2 = np.append(p2[1:], 0)
p3 = (p1 ^ p2) & 0xff
if not p3[0] == 0:
p3 = p3 ^ pr
poly_7.append(p3)
index = []
for i in range(len(poly_7[0])):
for j in poly_7:
if j[i] != 0:
index.append(i)
break
Polly_table = []
for i in range(256):
val = np.zeros(len(poly_7[0]), dtype='uint8')
for j in range(8):
if ((i >> j) & 0x1):
val = val ^ poly_7[j]
indexed_val = []
for k in index:
indexed_val.append(val[k])
Polly_table.append(np.array(indexed_val))
self.Polly_table = Polly_table
self.Polly_index = index
return 0
def modulus1 (self, A):
B = np.copy(A)
p1 = B.view('uint8')
p = p1[::-1]
byte_len = self.Polly_byte_len
bit_len = self.Polly_bit_len
while p[0] == 0:
if len(p) == 1:
break
p = p[1:]
'''Reduction based on lookup tables'''
while len(p) > byte_len:
red_poly = self.Polly_table[p[0]]
for j,k in zip(red_poly, self.Polly_index):
if j != 0:
p[k] ^= j
p = p[1:]
while p[0] == 0:
if len(p) == 1:
break
p = p[1:]
print p
while p[0] == 0:
if len(p) == 1:
break
p = p[1:]
if (len(p)+1 < self.Polly_index[-1]):
return p
r = p[0] & (gmpy2.bit_mask(bit_len-1) ^ 0xFF)
if r != 0:
'''Last byte reduction when polynomial is equal to primitive'''
if (len(p) == self.Polly_index[-1]):
red_poly = self.Polly_table[r]
for j,k in zip(red_poly, self.Polly_index):
if (k < len(p)):
p[k] ^= j
p[-1] ^= r
else:
'''Reduction by hand'''
while r != 0:
f_bit_pos = gmpy2.bit_length(r)
p1 = self.pr << (f_bit_pos -1)
p2 = self.pr >> (9 - f_bit_pos)
p1 = p1[:-1]
p2 = p2[1:]
p = p ^ p1 ^ p2
r = p[-1] & (gmpy2.bit_mask(bit_len-1) ^ 0xFF)
while p[0] == 0:
if len(p) == 1:
break
p = p[1:]
p = p[::-1]
q = np.append(np.zeros(4 - len(p)%4, dtype=np.int8), p)
q = np.array(q, dtype='uint8')
q = np.getbuffer(q)
q = np.frombuffer(q, dtype='uint32')
return q
def main():
print("##### Part 2 #####")
# get the modulo we want to factor from the command line
n = int(sys.argv[1])
gmpy2.get_context().precision = 4096
# variable to monitor when any process finishes
sync = multiprocessing.Event()
# Queue to hold the return value of the function so we can use it again in the main process
output_q = multiprocessing.Queue()
# check the factors of all numbers in batch
modulo = n
print("Attempting to find factors of", modulo)
bit_size = gmpy2.bit_length(gmpy2.mpz(modulo))
print("Modulo size:", bit_size)
curr_time = datetime.now().time()
print("Start Time:", curr_time)
# check if n is prime
if gmpy2.is_prime(modulo):
print("This probably shouldn't happen but n is prime", modulo)
return 0
# start PROCESS_COUNT amount of processes
for i in range(0, PROCESS_COUNT):
process = multiprocessing.Process(target=break_primes,
args=(modulo, i, sync, output_q))
PROCESSES.append(process)
process.start()
# wait until any of the processes find something then kill the others
sync.wait()
# kill the remaining processes once the factor has been found
for i in PROCESSES:
if DEBUG:
print("Killing processes")
i.terminate()
# join processes back to spawning process
for i in PROCESSES:
i.join()
# manage the queue so we can get returns from the processes
output_q.put('extra value to make the queue happy')
if DEBUG:
print("Queue Size", output_q.qsize())
# get the value back from the process
result = output_q.get()
if DEBUG:
print("Queue Size", output_q.qsize())
# clean up the queue
while not output_q.empty():
if DEBUG:
print("Cleaning")
output_q.get_nowait()
sync.clear()
# print ending time
curr_time = datetime.now().time()
print("End Time:", curr_time)
if DEBUG:
print("Factor of n is:", result)
def modulus1 (self, A):
B = np.copy(A)
p1 = B.view('uint8')
p = p1[::-1]
byte_len = self.Polly_byte_len
bit_len = self.Polly_bit_len
while p[0] == 0:
if len(p) == 1:
break
p = p[1:]
'''Reduction based on lookup tables'''
while len(p) > byte_len:
red_poly = self.Polly_table[p[0]]
for j,k in zip(red_poly, self.Polly_index):
if j != 0:
p[k] ^= j
p = p[1:]
while p[0] == 0:
if len(p) == 1:
break
p = p[1:]
print p
while p[0] == 0:
if len(p) == 1:
break
p = p[1:]
if (len(p)+1 < self.Polly_index[-1]):
return p
r = p[0] & (gmpy2.bit_mask(bit_len-1) ^ 0xFF)
if r != 0:
'''Last byte reduction when polynomial is equal to primitive'''
if (len(p) == self.Polly_index[-1]):
red_poly = self.Polly_table[r]
for j,k in zip(red_poly, self.Polly_index):
if (k < len(p)):
p[k] ^= j
p[-1] ^= r
else:
'''Reduction by hand'''
while r != 0:
f_bit_pos = gmpy2.bit_length(r)
p1 = self.pr << (f_bit_pos -1)
p2 = self.pr >> (9 - f_bit_pos)
p1 = p1[:-1]
p2 = p2[1:]
p = p ^ p1 ^ p2
r = p[-1] & (gmpy2.bit_mask(bit_len-1) ^ 0xFF)
while p[0] == 0:
if len(p) == 1:
break
p = p[1:]
p = p[::-1]
q = np.append(np.zeros(4 - len(p)%4, dtype=np.int8), p)
q = np.array(q, dtype='uint8')
q = np.getbuffer(q)
q = np.frombuffer(q, dtype='uint32')
return q
